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Standard Deviation Calculator

Calculate dispersion (spread) in your dataset.

Sample ($n-1$)
Population ($N$)
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Sample Standard Deviation
0.000
Variance (s2) = 0.000
Count (n)
0
Sum (∑x)
0
Mean (x̄)
0
Min / Max
0 / 0

Understanding the Results

Sample (s)

Use this mode when your data represents a subset of a larger population. This method uses Bessel's correction (dividing by n - 1), which provides an unbiased estimate of the population variance.

s = √ [∑(xi - x̄)2 / (n - 1)]

Population (σ)

Use this mode when you have data for the entire population (every possible data point). This method calculates the exact variance by dividing by N.

σ = √ [∑(xi - μ)2 / N]

What is Standard Deviation?

Standard deviation measures the amount of variation or dispersion in a set of values.

  • Low SD: Data points are close to the mean.
  • High SD: Data points are spread out over a wider range.

Variance

Variance is the square of the standard deviation. It represents the data points' spread from the mean, but in squared units (e.g., square dollars, square meters).

Variance = (Standard Deviation)2